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CA Foundation · Quantitative Aptitude · Equations

The cost of a cubic storage tank design at Patel Industries leads to the equation x³ − 9x = 0, where x is the side in metres. Which positive value of x is a valid side?

The valid side is 3 metres. Factorising x³ − 9x gives x(x − 3)(x + 3) = 0, so the roots are 0, 3 and −3. A side length must be positive and nonzero, leaving x = 3.

  1. Ax = 9
  2. Bx = 1
  3. Cx = 3Correct
  4. Dx = 0

Explanation

Factorise: x(x² − 9) = 0, so x = 0, 3 or −3. The only positive nonzero value is 3. Check: 27 − 27 = 0. The value 9 is wrong because it comes from treating x² = 9 as x = 9; 9³ − 81 ≠ 0.

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